Re: _Verum Et Factum Convertuntur_ (or: Surprised By Syntax)

In article <3gjd96Fck07bU1@xxxxxxxxxxxxxx>,
Harlan Messinger <hmessinger.removethis@xxxxxxxxxxx> wrote:
>Greg wrote:
>> Des Small wrote:

>>>Harlan Messinger <hmessinger.removethis@xxxxxxxxxxx> writes:


>>>>Herman Rubin wrote:

>>>>>When you have seen the collections of characters produced by
>>>>>college students claiming to be reasonably intelligent written
>>>>>communications, or heard the questions which are not intelligible
>>>>>because the words have nothing to do with any remotely reasonable
>>>>>understanding of the topic, youn will not take that position.

>>>>I'm starting to gather that you're deaf and signless and that to you
>>>>written language is the sum and substance of language.

>>>It seems that langwidge, for Herman, properly aspires to the condition
>>>of mathematics.

There are many others who consider language to be largely
grammar upon which a rather arbitrary vocabulary has be
added. Even with this arbitrariness, learning the
grammatical structure reduces the amount of vocabulary
which has to be learned, and if some etymology is learned,
this is reduced even more.

Despite the apparent variety of grammatical structures, the
structure of language does not vary THAT much, which is why
we can try to understand it.

>> As I read postings in this thread, I keep trying to deduce what the
>> posters think the difference is between natural language and
>> mathematics.

>Well, mathematics isn't language, so there's one substantial difference.
>Comparing natural language to mathematics is like comparing French to
>Poland.

Most of mathematics, in use, is language. I have
frequently stated that I would like students to be able to
formulate their problems, NOT to compute the answers. In
the practical problems of today, such as medical treatment,
the best-formulated problems are only going to be solved by
computers.

>And then there's Herman's lament that natural language isn't as precise
>as mathematics (by which, yes, I understand him to mean "mathematical
>representation"). Well, that *is* a *difference* between them, isn't it?
>Natural language relies on human psychology for interpretation.
>Mathematical representation doesn't.

It is unclear how much "human psychology" is needed for
interpretation of mathematics. Mathematical concepts are
not understood as collections of words, but as more than
that. One problem is that some concepts seem to have more
than one intensional attribute; for simple things like the
non-negative integers, the two basic ones are quite distinct,
and there are related versions of them. Students are taught
HOW to add, but not what addition means, and what it means
differs in the different intensional meanings.

Without these intensional understandings, the extensional
structures can be used, but the use can be totally missed.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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